JEE MAIN - Mathematics Hindi (2023 - 30th January Evening Shift - No. 1)
माना $$a_{1}=1, a_{2}, a_{3}, a_{4}, \ldots$$. क्रमागत धन पूर्णांक हैं। तब $$\tan ^{-1}\left(\frac{1}{1+a_{1} a_{2}}\right)+\tan ^{-1}\left(\frac{1}{1+a_{2} a_{3}}\right)+\ldots . .+\tan ^{-1}\left(\frac{1}{1+a_{2021} a_{2022}}\right)$$ बराबर है:
$$\frac{\pi}{4}-\cot^{-1}(2022)$$
$$\frac{\pi}{4}-\tan^{-1}(2022)$$
$$\cot^{-1}(2022)-\frac{\pi}{4}$$
$$\tan^{-1}(2022)-\frac{\pi}{4}$$
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